Water-Mediated Base Pairs in RNA – A Quantum-Chemical Study
M. Brandl, M. Meyer†, and J. Sühnel*
Biocomputing Group, Institute of Molecular Biotechnology, Beutenbergstr. 11, D-07745
Jena, Germany.
†
present address: Konrad-Zuse-Zentrum für Informationstechnik, Takustr.7, D-14195 BerlinDahlem, Germany
Received
*
Corresponding author: Jürgen Sühnel, e-mail: [email protected], FAX: +49-3641-656210
We have studied the geometric and energetic properties of the six water-mediated base pairs
WUC, WGA, WUA, WUU, WUG, WGG (W: water) and of the related water-free complexes
by quantum-chemical calculations including electron correlation at the MP2/631G(d,p)//HF/6-31G(d,p) and B3LYP/6-31G(d,p) levels. In the water-mediated WUC, WGA
and WUU base pairs water is both donor and acceptor of H-bonds and for these complexes the
calculated hydrogen bonding patterns are close to the experimental ones within the RNA helix
and allow cooperative effects within the H-bond network. The geometries of these base pairs
are obviously almost not affected by the nucleic acid and solvent environment. Therefore, they
can be considered as structurally autonomous building blocks of RNA. In the optimized
structure of the WUA base pair water still links the two bases, yet the H-bond pattern deviates
somewhat from the one in the RNA crystal structure and it is not cooperative. Therefore, we
classify the WUA base pair as an intermediate case. In WUG and WGG pairs water is twice
acceptor or twice donor. These complexes are not structurally autonomous, but apparently
have to be stabilized by additional interactions with the surrounding nucleic acid and solvent.
For the UG pair a water-mediated C5-H5(U)...O6(G) contact involving an alternative water
molecule (371) in the major groove is important and leads to a base pair geometry resembling
the experimental structure (W371UG). In the GG pair short contacts to a backbone C5’-H5’
donor group and to a further water molecule are likely to stabilize the experimental base pair
1
geometry. Similar to exocyclic amino groups water involved in base pairing induces nonplanar equilibrium geometries, yet except for one of the examples (WGA) the energy
difference to the corresponding planar conformation is very small. Cooperative effects have
been found to contribute between 9 and 13% at the MP2/HF level and between 8 and 20% at
the B3LYP level of the total interaction energy to all water-mediated pairs except for WUA.
WUC is the only example for which the absolute value of the total interaction energy per Hbond is significantly increasing in passing from the direct to the water-mediated pair.
Introduction
For a long time it has been assumed that at least two direct standard hydrogen bonds
(H-bonds) are necessary for base pair formation in nucleic acid structures.1,2,3 Recently,
however, base pairs have been detected that are linked by only one or even no standard Hbond. In these cases short N-H...F4,5, C-H...O6 and C-H...N7 contacts may replace
conventional H-bonds. In addition, the first examples of water-mediated base pairs have been
found.8-15 In these complexes direct base-base H-bonds within a base pair are accompanied by
an additional water-mediated link (Figure 1). We adopt the term water-mediated base pair
because it is used by structural biologists. In order to avoid confusion it should be pointed out
that the term describes a base complex with water incorporated within one and the same base
pair. It does not refer to water-mediated interactions between different base pairs. It should be
further noted that most X-ray structures do not provide hydrogen atom positions. Therefore,
the donor/acceptor properties of water have to be inferred from the corresponding base atom
types.
A water-mediated UC (WUC) base pair has been identified by Holbrook et al.8 within
the RNA duplex (r-GGACUUCGGUCC)2, where the central GU and UC mismatches do not
2
form an internal loop, but rather a highly regular helix (Figure 1a). The base pair is linked by a
direct H-bond between H42 of cytosine and O4 of uracil and a water-mediated H-bond
between H3 of uracil and N3 of cytosine. With 11.7 Å2 the water involved in this base pair
has the lowest temperature factor of all water molecules in the RNA structure, which suggests
that the water molecule is rather tightly bound. The WUC pair is also found in other structures
with the same core sequence CUUCGG 9,10.
Two additional water-mediated base pairs between two uracil bases (WUU) and
between uracil and adenine (WUA) have been described in the structure of glutaminyl-tRNA
complexed with its cognate aminoacyl-tRNA synthetase.11 The pairs are neighboring and
stacked on the anticodon stem and elongate the latter. Among the water molecules associated
with RNA only, the temperature factors (30.0 Å2) of the two water molecules involved in the
water-mediated base pairs are the forth lowest ones. Further water-mediated H-bonds link the
bases to the sugar moiety and to the protein. The WUU base pair exhibits direct H-bonding
between H3(U2) and O4(U1) and water-mediated H-bonding between H3(U1) and O2(U2)
(Figure 1b). There is some evidence in support of the fact the WUU base pair in glutaminyl
tRNA is actually a water-mediated pseudouracil-uracil base pair. Yet, uracil has been used
instead of pseudouracil in the PDB (Protein Data Bank) structure file. In other structures of
glutaminyl tRNA12,13 the problem has been treated in a similar way. NMR data suggest a
water-mediated base-base H-bond to occur in an RNA hairpin UU mismatch with the same Hbond pattern as for the WUU pair described above.14 In WUA there is a direct H-bond
between H62 of adenine and O2 of uracil. H3 of uracil is linked to N7 of adenine by a watermediated H-bond (Figure 1c).
Three other water-mediated base pairs have been identified within the internal loop E
of the 5S rRNA structure solved by Correll et al.15 In a water-mediated GA base pair (WGA)
the direct H-bond links H61 of adenine to O6 of guanine. H1 of guanine is connected to N1 of
adenine via a water molecule (Figure 1d). As in the case of WUC, the temperature factor
3
(19.6 Å2) of water involved in that H-bond is the lowest one found for water molecules within
the X-ray structure. In a water-mediated UG base pair (WUG), O4 of uracil is linked to H1
and H22 of guanine. A water molecule (temperature factor: 22.11 Å2) is H-bonded to N3-H3
of uracil (Figure 1e) and has been claimed to be also acceptor of an H-bond with H22 of
guanine as the donor. In a water-mediated GG base pair (WGG) O6 of one guanine is linked
to the H1 and H22 hydrogens of the other guanine. The N7 and O6 atoms are connected by a
water molecule, which is assumed to donate two H-bonds to the bases (temperature factor:
22.11 Å2; Figure 1f). The H-bond patterns of the WUC, WGA, WUG and WGG base pairs
have also been discussed in a review on base pair hydration.16
Thus far, we do not know, whether these new unusual base pairs are only possible
within the specific environment where they have been found, or whether they represent
structurally autonomous nucleic acid building blocks that do not depend on additional
stabilization by the surrounding backbone or by neighboring base pairs. Quantum-chemical ab
initio calculations with the inclusion of electron correlation energy have provided a rather
consistent view of the features of canonical and noncanonical base pairs linked by at least two
direct standard H-bonds.17,18 According to these calculations the equilibrium geometries of
Watson-Crick, wobble, Hoogsteen and other base pairs that have been determined without
considering the sugar-phosphate backbone closely resemble the experimental base pair
geometries within the complete nucleic acid. Obviously, the base pair geometry is almost not
affected by stacking effects or by interactions exerted by the nucleic acid backbone. Therefore,
these base pairs can be regarded as structurally autonomous nucleic acid building blocks.
Recently, we have shown that this also applies to the WUC complex.19 In this work we extend
this study and report on a comprehensive quantum-chemical analysis of the geometries and
interaction energies of six water-mediated base pairs.
Methods
4
For the quantum-chemical calculations only the base parts of the nucleotides have been
used. As in the studies of Šponer et al.17 the sugar moieties were replaced by hydrogens. The
Protein Data Bank (PDB)20 and Nucleic Acid Database (NDB)21 codes of the RNA structures
with the water-mediated base pairs are: 165d/ahib53, 255d/arl037, 373d/arm0107,
413d/ar0005 (RNA duplex8-10); 1gtr/ptr0003, 1gts/ptr0002 (glutaminyl-tRNAsynthetase/tRNA complex11); 354d/url064 (loop E from E.coli 5S rRNA15). In the paper on
the X-ray structure of glutaminyl-tRNA water-mediated base pairs between pseudo-uracil and
2’-O-methyl-uracil and between uracil and 2-methyl-adenine are described.11 The
corresponding PDB entry 1gtr, however, contains standard nucleotides instead of modified
ones and therefore we have used the standard bases for our calculations (WUU, WUA).
The properties of the water-mediated and of the related direct base pairs have been
calculated adopting Hartree-Fock (HF) and density functional theory (DFT) approaches. The
geometries of all complexes have been optimized at the HF/6-31G(d,p) and at the density
functional B3LYP/6-31G(d,p) level. Interaction energies of structures obtained at the HF/631G(d,p) level have been calculated using the MP2(FC)/6-31G(d,p) method (FC: frozen core).
DFT interaction energies have been determined at the B3LYP/6-31G(d,p) level. Energy
minima have been verified by calculation of the Hessian. The interaction energies ∆E have
been corrected for the basis set superposition error (BSSE) according to the standard
counterpoise method.22 A further correction was done for the deformation energies ∆EDEF,
which are defined as the energy differences between the geometries of the optimized
monomers and the structures of the monomers adopted in the complex. Interaction energies
taking into account deformation energies have been denoted as ∆ET.
∆EΤ=∆E+Σ∆EDEF
5
Finally, for the calculation of the total interaction energy ∆E0 at the HF/6-31G(d,p),
MP2(FC)/6-31G(d,p)//HF/6-31G(d,p) and the B3LYP/6-31G(d,p) levels the changes in zeropoint energy ∆EZPE have been considered.
∆E0=∆ET+∆EZPE
The zero point energy terms at the HF/6-31G(d,p) and B3LYP/6-31G(d,p) levels have
been corrected using scaling factors of 0.9135 and 0.9804, respectively.23 In order to estimate
the energy difference between optimal nonplanar and planar structures all direct and watermediated base pairs have also been optimized with the restraint of planarity. Interaction
energies are discussed using ∆E0. The zero-point energy change cannot be computed,
however, for planar structures that do not correspond to an energy minimum. In this case ∆ET
is used.
For complexes consisting of three components A, B, and C the interaction energy ∆E
can be understood as the sum of three pairwise dimer contributions and a three-body term ∆E3
that accounts for cooperative effects.24
∆EABC = ∆EAB + ∆EAC + ∆EBC + ∆E3
The interaction energies have been calculated within the geometry of the optimized
trimer and were corrected for the basis set superposition error in the trimer-centered basis set.
All ab initio calculations have been performed with the GAUSSIAN 94 package.23
The occurrence of unusual base pairs in the database of three-dimensional RNA
structures has been investigated using our program BP-FINDER, which identifies base pairs
according to the approximate coplanarity of the constituent bases, and subsequent inspection
of the hits within their nucleic acid environment. For the identification of H-bonds a cutoff of
6
3.0 Å for the distance between the hydrogen atom and the acceptor has been used.
Results and Discussion
Geometry and structural autonomy. The geometries of the water-mediated basepairs have been optimized at the HF/6-31G(d,p) and B3LYP/6-31G(d,p) levels (Tables 1-5).
Apart from systematic differences concerning the inter-base plane angles and H-bond lengths
very similar results have been obtained. Usually, the results obtained by HF optimization are
closer to the experimental data than the DFT results. For the WUC, WUU, and WGA
complexes, in which the water molecule links H-bond donor and acceptor groups and acts
both as an H-bond donor and acceptor, we have obtained stable complexes with geometry
parameters close to the values found in the experimental structures (Figures 2 a, c, e; Tables 13). This suggests, that the WUC, WUU and WGA pairs represent structurally autonomous
building blocks of RNA. Within the optimized WUA complex water still links the two bases
but the H-bond pattern is slightly different to the experimental one. (Figures 1c, 2g; Table 4).
Moreover, the direct H-bond is rather long. Therefore, WUA should be classified as an
intermediate case. Finally, geometry optimizations of WUG with water as double H-bond
acceptor and WGG with water as double H-bond donor did not lead to minimum structures in
which water bridges the two bases. In this context it is interesting to note that for water
trimers a highly cooperative “head to tail” - arrangement, in which all water molecules act
both as donors and acceptors of H-bonds, is the most favorable structure. Other cyclic
configurations with water acting as double donor or acceptor are substantially less favorable
or do not correspond to minima at all.25,26
We have looked for additional interactions that might stabilize the WUG and WGG
base pair structures observed in the RNA crystal structure. Closer inspection of the UG
mismatch shows that the water molecule 371 at the major groove side of the base pair is
7
linked to guanine by an O-H...O6(G) standard H-bond and to the C5-H5 group of uracil by a
C-H...O contact (Figure 3a). In contrast to H2O 329, H2O 371 acts both as a donor and
acceptor of H-bonds. Optimization of the triplex consisting of G, U and water 371 (W371UG;
Figure 2i) and of the related direct UG base pair (Figure 2j) has shown that the experimental
base pair geometry (Figure 3a) is closer to the structure of the water-mediated base pair than
to the structure of the direct base pair (Figures 4a, b; Table 5). Obviously, water 371 acts as a
spacer that widens the major groove oriented part of the base pair and thus prevents the
formation of a direct base pair. The C5(U)...O(H2O) contact in the experimental structure is
considerably longer than in the optimized simplified model. Therefore, it is not likely to
contribute significantly to the overall stability of the complex. Nonetheless, water 371
obviously plays a role in maintaining the experimental base pair geometry. Recently, C-H...O
interactions have been claimed to represent a long-neglected stabilizing force in
biopolymers.27 The C5-H5 group of uracil has already been found to be involved in a C-H...O
contact within the Calcutta UU base pair, which is formed as a crystal contact between two
RNA strands with 5'UU overhangs.6 Furthermore, the C5-H5 group of pyrimidines has been
suggested to play a role in RNA hydration28 and protein/DNA recognition.29 It should be
noted, however, that C-H...O interactions may be enforced by strong neighboring interactions
in an opportunistic manner. The C-H...O contact in W371UG might represent an example for
the structural role of these interactions in biopolymers. As already noted, geometry
optimization also failed for WGG in which water acts as double donor, even though in the
experimental structure both H-bonds involving H2O 330 exhibit standard distances (Figure
3b). In the RNA crystal structure H2O 330 is coordinated to H2O 312 (O...O distance: 2.63 Å)
and to the backbone C5’-H5’ group of the previous nucleotide (C5’-H5'....O (H2O 330)
distance: 2.49 Å). Systematic searches for short C-H...O and C-H...N contacts in experimental
RNA structures7 and molecular dynamics simulations of the FMN binding RNA aptamer30
have shown that the C5’-H5' group is a C-H donor with similar features as the previously
8
found C2'-H2' donor groups.31 Therefore, we think, that the additional contacts shown in
Figure 3b are candidates for base pair stabilization. Due to the complexity of the system the
coordination of H2O 312 to H2O 330 and to C5’-H5’ of A99 could not be confirmed by
quantum-chemical calculations.
In order to study how the insertion of a water molecule changes the base pair shape we
have calculated the geometries of direct base pairs formed upon removal of the water
molecule. Both HF and DFT optimizations lead to stable structures in all six direct base pairs
(Figures 2b, d, f, h, j, k).
All water-mediated base pairs are nonplanar (Figure 2; Tables 1-5). The calculated
inter-base plane angle depends in a rather sensitive manner on the calculation approach and is
in all cases larger than found in the experimental structure. The deviations from planarity are
mainly of the buckle type and caused by the sp3 hybridization of water and by the nonplanarity
of the amino groups. The direct UA and UU base pairs are planar, whereas UC and GA
exhibit propeller twists and UG and GG are slightly buckled (Figure 2). Repulsion between
O2(C)/O2(U), H22(G)/H2(A) and H3(U)/H22(G) contributes to the nonplanarity in the direct
UC, GA, UG base pairs, which is likely to alleviate the insertion of water molecules. Another
contribution stems from the nonplanarity of the exocyclic amino-groups in C, G and A.
In an ideal RNA helix the C1’-C1’ distances within Watson-Crick base pairs are 10.4
Å (AU) and 10.7 Å (GC).32 With 8.8, 8.7 and 9.7 Å the corresponding distances (HF level) for
the UC, UU and UA complexes, respectively, are shorter than the standard value, whereas the
corresponding distances for GA (13.1 Å), UG (12.6 Å) and GG (11.16 Å) are longer (Tables
1-6). For each mismatch the C1’-C1’ distances are increased by the formation of watermediated base pairs. Thus, for WUC, WUU and WUA inclusion of water leads to C1’-C1’
distances that are closer to the standard RNA geometry, whereas the opposite is true for WGA
and W371UG.
9
Interaction energy and cooperativity. The interaction energies ∆E0 of the watermediated base pairs range from -13.2 to -20.2 kcal/mol (MP2/HF) (Table 7). For the direct
base pairs energies between -8.7 and –15.7 kcal/mol have been found. For almost all base
pairs inclusion of electron correlation at either MP2 or DFT levels increases the absolute
values of interaction energies, cooperativity terms and deformation energies as compared to
the HF values.
It is likely that insertion of a nonplanar base pair into a double helical environment
requires a (partial) planarization of the base pair. In order to estimate the energy that is needed
to enforce planarity, we have compared the total energies ∆ΕΤ of the planar conformation to
the respective energies of the optimal nonplanar conformations (Table 7, column 11). Except
for the WGA base pair the energy differences between the optimal nonplanar and the planar
structures are rather small. Thus, the energy barrier of a partial planarization of the base pairs
which is very likely to occur upon incorporation of the base pairs into a nucleic acid helix
environment can easily be overcome.
Nonplanarity of nucleic acid base pairs is well-known from other quantum-chemical
studies.33 It is assumed to be primarily due to a partial sp3 hybridization of the amino group
nitrogen atom. For GA base pairs the difference in the total energy between the planar and
optimal structures has been found to vary between 0.1 and 1.8 kcal/mol. One of these base
pairs (GA-I) can directly be compared to the direct GA pair studied in this work. We find as
energy difference 0.8 and 1.9 kcal/mol at the HF and MP2/HF levels, respectively (Table 7).
This is in line with the value of 0.8 kcal/mol given by Šponer et al.32 Except for the WGA
complex the energy preference for the nonplanar structrures of water-mediated base pairs is of
the same order of magnitude as for nonplanar pairs with direct H-bonds. Finally, it should be
noted that even though a partial planarization of water-mediated base pairs upon incorporation
10
into a nucleic acid double-helix helix is very likely, it cannot be excluded that they can
become even more nonplanar in certain circumstances.
A further property that may be important for folding and recognition is base pair
flexibility. This cannot directly be addressed by quantum-chemical studies. We have,
however, performed a molecular dynamics simulation of the RNA duplex (rGGACUUCGGUCC)2 with two water-mediated UC pairs. Indeed, we find that the watermediated pairs are much more flexible than the other Watson-Crick and GU pairs in the
duplex (C. Schneider, M. Brandl, J. Sühnel; unpublished results).
Except for the WUA case all water-mediated base pairs are stabilized by cooperativity.
At the MP2/HF level the corresponding energy terms ∆E3 are between -1.8 kcal/mol for WUU
and -3.2 kal/mol for WGA and contribute between 9 and 12% to ∆E. At the B3LYP/631G(d,p) level cooperative contributions of up to 20% of the total interaction energy have
been obtained (Table 8). Cooperativity has been investigated for H-bonded trimers of nucleic
acid bases and found to be negligible for most uncharged structures.24 The only exception was
the GGC Hoogsteen trimer structure with a cooperativity term of -4 kcal/mol. In contrast to
these base triplexes water-mediated base pairs are significantly stabilized by cooperativity. In
each system the interaction energies within the water-mediated three-component systems are
more negative than in the two-component direct systems. This is due to the additional H-bond
and to cooperativity. With -8.6 and -7.6 kcal/mol at the MP2/HF level the WUC and WGA
mismatches show the largest differences in interaction energies between direct and watermediated base pairs (Table 9). In these base pairs the water-mediated conformations show
highly cooperative networks of strong H-bonds, whereas the direct UC and GA base pairs are
somewhat weakened by O2(U)/O2(C) and H22(G)/H2(A) repulsion. With -5.9 and -5.5
kcal/mol the difference in the W371UG and WUU cases is less pronounced and the
cooperativity terms are slightly smaller than for the WUC and WGA complexes. In these
cases the water-mediated base pairs include the weak C5-H5(U)...O(H2O) contact (W371UG)
11
and the relatively weak H(H2O)...O2(U) H-bond (WUU), which can account for decreased
cooperativity values. Finally, for the WUA base pair the interaction energy has been found to
be only -2.0 kcal/mol larger than that of the direct base pair, which is due to the very weak
interaction between U and A and the absence of cooperativity. WUA differs from the other
water-mediated base pairs in the respect that both bases are twice bound to water and only
weakly H-bonded with each other. Furthermore the H3 proton of U and the H62 proton of A
are in tight proximity and likely to repel each other. Because of the deviations of the WUA
base pair geometry from the experimental one and the lack of cooperativity in WUA we
classify the WUA base pair as an intermediate case between the structurally autonomous and
fully cooperative WUC, WUU, WGA and W371UG base pairs and the WGG base pair, which
depends on structural support from the nucleic acid environment.
In order to get a rough estimate of varying average H-bond strengths in passing from
direct to water-mediated pairs we have divided the total interaction energy by the number of
H-bonds. Bifurcated H-bonds have been considered as one single H-bond for that purpose
(Table 10). It turns out that in all water-mediated pairs with a substantial cooperative effect
the absolute values of the interaction energy per H-bond increases. The only example with a
decrease is WUA which exhibits no cooperativity. However, the increase in WUU, WGA and
W371UG is only relatively small (0.11 – 0.43 kcal/mol). The only case in which the inclusion
of water leads to a substantial increase in H-bond strength is the WUC base pair. A possible
explanation for this pattern is the destabilization of the direct UC base pair caused by the
O2(C)…O2(U) repulsion and reflected by the rather long 2.14 Å H-bond distance between
N3-H3(U) and N3(C) (Fig 2b). UC is the only direct base pair in which an H-bond is
significantly weakened by intermolecular repulsion exerted by adjacent functional groups.
A comparison between the two water-mediated pyrimidine-pyrimidine base pairs
WUC and WUU shows that the interaction energy in WUC is by about -4 to -7 kcal/mol more
negative than for WUU. The difference in interaction energies stems from an increased
12
strength of the direct H-bond in WUC as compared to WUU, increased cooperativity and
predominantly from the difference between the strengths of the H(H2O)...N3(cytosine) and the
H(H2O)...O2(uracil) interaction. The charge patterns in WUC and WUU clearly indicate that
the H-bond accepting aza-nitrogen in C is more negative than the carbonyl oxygen in U and
this can account for the observed energy differences. Within the two water-mediated
pyrimidine-purine base pairs WUA and W371UG the differences in interaction energies are
similar as for WUC and WUU (-5 to -8 kcal/mol, depending on the method). The largest
interaction energies were found for WGA, which is due to the size of the complex and to the
strong H-bond network similar to the one in WUC.
Finally, it should be mentioned that interaction energies within the WUG, WGG and
WGA base pairs might be modified by Mg2+ ions that are bound to the N7 atoms of guanine
via their hydration shell.15 Quantum-chemical studies have indicated that the hydrated metal
ions increase the interaction energy of GG and GC pairs but do not enhance the strength of
base pairing in AA and AT pairs.34,35 Whether the metal ions affect the new types of base
pairs remains to be clarified.
Occurrence of water-mediated and related direct base pairs in three-dimensional
RNA structures. In order to detect further occurrences of water-mediated base pairs we have
first scanned all currently available experimental RNA structures deposited at the PDB for
base pairs, in which both bases contain a potential donor/acceptor site which is within a
distance of less than 3.5 Å to the oxygen of the same water molecule. Apart from some hits
obtained for water molecules located at the periphery of Watson-Crick GC base pairs no cases
of additional water-mediated base pairs could be identified.
Furthermore, we have scanned the same structures for the direct H-bond present in the
known water-mediated base pair or the two H-bonds present in the direct pairs. This enables
the identification of potential water-mediated base pairs in structures where the positions of
13
water molecules could not be determined. In addition, information on preferences for either
water-mediated or related direct base pairs in the currently known experimental structures is
obtained.
WUC base pairs could only be identified in the already mentioned structures with the
same core sequence as in the Holbrook dodecamer.8-10 No example for the related direct UC
base pair has been found.
The water-mediated WUU base pair has only been found in structures including
tRNAGlu (1gtr11, 1gts11, 1qrs12, 1qrt12, 1qru12, 1qtq13). The related direct UU base pair has
been identified in synthethic double stranded RNA oligomers with central UU mismatches
(205d36, 280d37), 5S rRNA helix I (1elh38), the U2 small nuclear RNA hairpin (1a9n39) and an
aminoglycoside binding RNA aptamer (1tob40).
The direct reverse Hoogsteen UA base pair has been found in different RNA
molecules including the loop E region of E.coli 5S rRNA (PDB codes: 354d15, 1a4d41), the
tRNA parts of complexes with aspartyl-tRNA synthetase (1asz42), glutaminyl-tRNA
synthetase (1qtq13), phenylalanine-tRNA (1tra43, 1ttt44), yeast initator tRNA (1yfg45) and an
FMN-RNA aptamer (1fmn46). Apart from its identification in the glutaminyl-tRNA
synthetase/tRNA complex (1qtq13), a possible WUA base pair was found between U 31 and A
8 in most of the models of the solution structure of the hairpin ribozyme loop B domain
(1b3647), where it is flanked by noncanonical GA and AA base pairs.
Direct GA base pairs are regularly occurring mismatches. Structure examples include
synthetic duplexes (157d48, 1mis49, 1mwg50), the complexes of tRNA with aspartyl tRNAsynthetase (1asy51) and glutaminyl tRNA-synthetase (1gts11), HIV-REV (1ebq52), aptamers
(1eht53, 1fmn46) and the group I intron ribozyme (1gid54). The WGA base pair has only been
found in loop E of 5S rRNA. For loop E of 5S rRNA both an X-ray and an NMR structure are
available (PDB codes: 354d15, 1a4d41). Even though in the NMR refinement process explicit
water molecules are not taken into account, for the WGA pair the distance between the base
14
donor and acceptor groups forming the water-mediated link N1-H(G)...N1(A) is
approximately the same as in the X-ray structure (difference: 0.04 Å). On the other hand, the
related distances for the WGG and WUG pairs differ significantly. Whereas, the
O6(G)...N7(G) distance is 1.34 Å longer in the X-ray structure than in the NMR structure, the
N3-H(U)...H-N2(G) distance is shorter by 1 Å. We believe that this observation confirms our
results. The WGA pair is a structurally autonomous building block and should thus not be
affected too much by possible differences between the NMR and X-ray structures. On the
other hand, the WUG and WGG pairs require additional stabilizing interactions including CH...O contacts. The C-H...O contacts are weak and may be either absent in the NMR structure
or not properly taken into account in the refinement.
Another direct UG base pair occurs within the structure of the group I intron ribozyme
(1gid54, 1grz55). Structures with UG base pairs that exhibit the bifurcated direct H-bond
observed in WUG, but with H5(U)...O6(G) distances longer than 6 Å (distance in WUG: 4.9
Å), were identified in the complex of tRNA with aspartyl tRNA-synthetase (1asy51) and
Thermus flavus 5S rRNA (361d56).
The direct GG base pair has been found in the structure of an ATP-binding RNA
aptamer (1raw57). The water-mediated WGG base pair could only be identified in the X-ray
structures of the 5S rRNA loop E. A GG base pair with a very large N7(G1)...O6(G2) distance
has been identified in the FMN-RNA aptamer structure (1fmn46) where it is flanked by a GA
base pair and FMN.
This analysis shows that so far water-mediated base pairs in RNA are only rarely
observed. The only example where base pairs of this type might have been overlooked is a UA
pair in the NMR structure of the hairpin ribozyme loop B domain.47 In almost all cases both
the water-mediated and the related direct base pairs occur and the latter ones are found more
frequently. An exception is the WUC pair, where only the water-mediated structure is known
thus far in three-dimensional RNA structures.8-10 When finalizing this work the structure of
15
the 23S rRNA sarcin/ricin domain has been reported, which includes water-mediated UC and
AC base pairs.58 The water-mediated UC base pair differs from the WUC base pair we have
studied insofar as the cytosine is oriented in a different way towards uracil. The AC pair is
unusual in that it has no direct H-bonds.
Relation to thermodynamics of base pairing. Thermodynamic studies on the
stabilities of RNA oligomers (absorbance versus temperature melting curves) have shown that
the total free energy of RNA duplex formation can be approximated as a sum of nearestneighbor increments.59 By means of this approach it has been found, for example, that
symmetric tandem UC mismatches destabilize an RNA helix.60 It should be noted that the
nearest-neighbor increments cannot be directly related to the interaction energies calculated in
this study. These energies constitute only one part of those increments. The other part is
composed of stacking energies with neighboring base pairs, interactions involving the
backbone, solvent and entropic effects. Entropic effects are especially important for watermediated base pairs because their formation requires the removal of a water molecule from the
bulk. Our calculations can, however, elucidate the energy contribution arising from the
intrinsic base pair properties. They can check whether water-mediated base pairs within RNA
are close to their ideal geometry and to what extent they are altered by external forces. In this
way they can contribute to a better understanding of the thermodynamic quantities within the
nearest-neighbor model.
Conclusions
The geometric and energetic properties of six water-mediated base pairs have been
studied by quantum-chemical ab initio calculations. In the water-mediated WUC, WGA and
WUU base pairs water is both donor and acceptor of H-bonds and for these complexes the
calculated hydrogen bonding patterns are close to the experimental ones within the RNA helix
16
and allow cooperative effects within the H-bond network. Therefore, WUC, WUU and WGA
can be considered as structurally autonomous building blocks which are expected to occur in
other nucleic acid environments as well. In the optimized structure of the WUA base pair
water still links the two bases, yet the H-bond pattern deviates somewhat from the one in the
RNA crystal structure and it is not cooperative. Therefore, we classify the WUA base pair as
an intermediate case between the structurally autonomous WUC, WGA and WUU base pairs
and the WUG and WGG base pairs.
In WUG and WGG pairs water is twice acceptor or twice donor. These complexes are
not structurally autonomous, but have to be stabilized by additional interactions. For the GU
pair a water-mediated C5-H5(U)...O6(G) contact involving a water molecule (371) in the
major groove is important and leads to a base pair geometry resembling the experimental
structure (W371UG). In the GG pair short contacts to a backbone C5’-H5’ donor group and to
a further water molecule are likely to stabilize the experimental base pair geometry.
The optimized geometries of all water-mediated base pairs are nonplanar. In most
cases the calculated inter-base plane angle is larger than found in the experimental nucleic
acid structure and strongly dependent on the calculation approach. However, except for WGA
the energy difference between the optimized nonplanar and planar structures is small.
Therefore, for most base pairs the planarization occurring on insertion of the base pair into the
nucleic acid should easily be possible.
The WUC, WUU, WGA and W371UG pairs are substantially stabilized by
cooperativity. From a comparison of the C1’-C1’ distances in the water-mediated and in the
alternative direct base pairs it turns out, that for UC, UU and UA the water-mediated
complexes have a geometry which is more similar to ideal Watson-Crick base pairs than that
of the direct ones. For the other base pairs the opposite is true. The structurally autonomous
water-mediated base pairs extend the alphabet of known base pairs and can play similar roles
in biological structures and processes as other canonical and noncanonical base pairs.
17
However, inclusion of water changes the base pair properties and creates a new motif which is
important for recognition by nucleic acids or proteins.
For all water-mediated and direct base pairs investigated the B3LYP results H-bond
pattern, planarity and cooperativity are similar to HF geometries and MP2/HF energies.
Supporting Information Available: Energies of water-mediated and direct base pairs
optimized at the HF, MP2/HF and B3LYP levels and the 6-31G(d,p) basis set. The material is
available free of charge via the Internet at http://pubs.acs.org.
Acknowledgement. This work was supported by a grant from the Thüringer Ministerium für
Wissenchaft, Forschung und Kultur (TMWFK).
18
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22
Figure captions
Figure 1. Chemical formulas of water-mediated base pairs: (a) WUC8-10, (b) WUU11, (c)
WUA11, (d) WGA15, (e) WUG15 and (f) WGG.15
Figure 2. Ab initio HF/6-31G(d,p) optimized geometries of water-mediated and direct base
pairs: (a) WUC, (b) UC, (c) WUU, (d) UU, (e) WGA, (f) GA, (g) WUA, (h) UA, (i) W371UG,
(j) UG, (k) GG. Optimization of the WUG pair shown in Figure 1e does not lead to a
minimum. Taking into account water 371, which is located at the major groove (Figure 3a),
leads to the stable structure shown in (Figure 2i). Similar to WUG, the WGG base pair shown
in Figure 1f is not stable, yet in this case no alternative water-mediated base-base link could
be identified.
Figure 3. Experimental geometries of the WUG and WGG base pairs within E. coli 5S rRNA
loop E (Protein Data Bank entry: 354d15; hydrogen atoms added with InsightII, Molecular
Simulations Inc.): (a) UG pair linked to water 329 and water 371; (b) WGG pair including the
structural water 330, which is coordinated to water 312 and to the C5’-H5’ backbone group of
A 99.
Figure 4. Superposition of the experimental W371UG structure 15 (black) with
a) optimized (HF/6-31G(d,p)) W371UG triplex (grey),
b) optimized (HF/6-31G(d,p)) direct UG base pair (grey).
23
TABLE 1: Calculated and Experimental Geometry Parameters in the Water-Mediated
(WUC) and the Related Direct UC Base Pairs
WUC
Distance / Å
UC
expa
calc
calc
HFb
DFTc
HFb
DFTc
O4(U)...H42(C)
-
2.02
1.87
1.97
1.82
O4(U)...N4(C)
2.7
2.98
2.85
2.97
2.85
H3(U)...O(H2O)
-
1.84
1.67
-
-
N3(U)...O(H2O)
2.8
2.85
2.72
-
-
H(H2O)...N3(C)
-
1.99
1.81
-
-
O(H2O)...N3(C)
2.8
2.95
2.80
-
-
H3(U)...N3(C)
-
4.05
3.66
2.14
1.92
N3(U)...N3(C)
4.7
4.83
4.48
3.14
2.96
O2(U)...O2(C)
6.8
6.79
6.18
3.73
3.49
C1’(U)...C1’(C)
11.7
11.69
11.09
8.79
8.59
Base plane angle / º
12
18
30
26
25
a
Experimental structure: PDB code: 255d.8
b
HF/6-31G(d,p).
c
B3LYP/6-31G(d,p).
24
TABLE 2. Calculated and Experimental Geometry Parameters in the Water-Mediated
(WUU) and the Related Direct UU Base Pairs
WUU
Distance / Å
expa
UU
calc
calc
HF
DFT
HF
DFT
O4(U1)...H3(U2) b
-
1.93
1.87
1.99
1.84
O4(U1)...N3(U2)
3.1
2.93
2.90
2.98
2.87
H3(U1)...O(H2O)
-
1.91
1.79
-
-
N3(U1)...O(H2O)
3.1
2.89
2.77
-
-
H(H2O)...O2(U2)
-
1.99
1.89
-
-
O(H2O)...O2(U2)
3.1
2.93
2.80
-
-
O2(U2)...H3(U1)
-
4.15
3.00
1.99
1.84
O2(U2)...N3(U1)
5.1
4.80
3.67
2.97
2.87
C1’(U1)-C1’(U2)
11.5
11.06
9.35
8.66
8.57
Base plane angle / °
14
9
39
0
0
a
Experimental structure, PDB code: 1gtr.11 b The definition of U1 and U2 is given in Figure 1.
25
TABLE 3. Calculated and Experimental Geometry Parameters in the Water-Mediated
(WGA) and the Related Direct GA Base Pairs
WGA
Distance / Å
expa
GA
calc
calc
HF
DFT
HF
DFT
O6(G)...H61(A)
-
2.03
1.86
2.00
1.83
O6(G)...N6(A)
3.0
2.98
2.83
3.00
2.86
H1(G)...O(H2O)
-
1.94
1.81
-
-
N1(G)...O(H2O)
2.8
2.92
2.80
-
-
H(H2O)...N1(A)
-
1.93
1.72
-
-
O(H2O)...N1(A)
2.8
2.89
2.73
-
-
H22(G)...O(H2O)
-
2.37
2.20
-
-
N2(G)...O(H2O)
3.5
3.20
3.05
-
-
H1(G)...N1(A)
-
3.78
3.55
2.07
1.89
N1(G)...N1(A)
4.8
4.60
4.40
3.08
2.93
H22(G)...H2(A)
-
5.11
4.79
2.60
2.42
C1’(G)...C1’(A)
14.8
14.13
13.99
13.07
13.00
35
36
22
18
Base plane angle / ° 7
a
Experimental structure, PDB code: 354d.15
26
TABLE 4. Calculated and Experimental Geometry Parameters in the Water-Mediated
(WUA) and the Related Direct UA Base Pairs
WUA
Distance / Å
expa
UA
calc
calc
HF
DFT
HF
DFT
O2(U)...H61(A)
-
3.19
3.19
2.17
2.00
O2(U)...H62(A)
-
2.61
2.35
3.66
3.52
O2(U)...N6(A)
2.8
3.22
3.08
3.16
3.01
H3(U)...H61(A)
-
2.35
2.17
2.86
2.79
N3(U)...N6(A)
5.0
3.73
3.54
4.27
4.16
H(H2O)...N7(A)
-
2.10
1.91
-
-
O(H2O)...N7(A)
3.3
3.01
2.85
-
-
O(H2O)...H61(A)
-
2.27
2.10
-
-
O(H2O)...N6(A)
5.5
3.22
3.06
-
-
H3(U)...O(H2O)
-
2.03
1.90
-
-
N3(U)...O(H2O)
3.1
2.95
2.84
-
-
H(H2O)...O4(U)
-
2.27
2.04
-
-
O(H2O)...O4(U)
3.8
3.03
2.90
-
-
H3(U)...N7(A)
-
4.33
3.92
1.94
1.81
N3(U)...N7(A)
4.7
5.19
4.81
2.94
2.77
C1’(U)-C1’(A)
9.8
11.17
10.65
9.73
9.67
63
69
0
0
Base plane angle / ° 9
a
Experimental structure, PDB code: 1gtr.11
27
TABLE 5. Calculated and Experimental Geometry Parameters in the Water-Mediated
(W371UG) and the Related Direct UG Base Pairs
W 371UG
Distance / Å
expa
UG
calc
calc
HF
DFT
HF
DFT
O4(U)...H1(G)
-
2.13
2.05
1.99
1.88
O4(U)...N1(G)
2.9
3.05
2.95
2.97
2.88
O4(U)...H22(G)
-
2.09
1.96
2.46
2.38
O4(U)...N2(G)
3.0
3.00
2.88
3.29
3.22
H5(U)...O(H2O)
-
2.21
2.01
-
-
C5(U)...O(H2O)
3.9
3.28
3.10
-
-
H(H2O)...O6(G)
-
1.93
1.79
-
-
O(H2O)...O6(G)
2.8
2.87
2.76
-
-
H5(U)...O6(G)
-
3.88
3.97
2.36
2.19
C5(U)...O6(G)
-
4.75
4.85
3.41
3.26
C1’(G)-C1’(U)
13.1
13.15
13.11
12.55
12.45
13
17
4
9
Base plane angle / ° 9
a
Experimental structure, PDB code: 354d.15
28
TABLE 6. Calculated and Experimental Geometry Parameters in the Water-Mediated
(WGG) and the Related Direct GG Base Pairs
Distance / Å
WGG
GG
expa
calc
HF
DFT
O6(G1)...H22(G2) b
2.0
2.31
3.17
O6(G1)...N2(G2)
2.9
3.28
2.17
O6(G1)...H1(G2)
1.9
3.65
3.56
O6(G1)...N1(G2)
2.8
4.36
4.26
N7(G1)...O(H2O)
2.8
-
-
O(H2O)...O6(G2)
2.8
-
-
N7(G1)...H1(G2)
4.1
1.96
1.83
N7(G1)...N1(G2)
5.1
2.96
2.85
C1’(G1)-C1’(G2)
13.6
11.16
11.10
Base plane angle / °
10
2
9
a
Experimental structure, PDB code: 354d.15
b
The definition of G1 and G2 is given in Figure 1.
29
TABLE 7. Interaction Energies (kcal/mol) for Water-Mediated (WXY) and the
Corresponding Direct (XY) Base Pairs Calculated According to the HF, MP2/HF, and
DFT Approaches a
(W)XY
∆E
∆EXY ∆EXW ∆EYW ∆E3
∆EDEF(X)
∆EDEF(Y) ∆EDEF(W) ∆ET
E-Epla
∆EZPE ∆E0
e
f
g
h
i
0.5
0.1
-19.5
-0.1
3.4
-16.1
0.6
0.5
0.1
-21.6
-0.5
3.4
-18.2
-5.3
1.6
0.9
0.3
-23.2
3.3
-20.0
-
-
0.8
0.3
-
-8.8
-0.1
1.3
-7.5
-
-
-
0.8
0.3
-
-10.8
-0.3
1.3
-9.6
-
-
-
-
1.4
0.7
-
-11.2
-
1.0
-10.2
-16.0
-4.2
-5.8
-4.2
-1.7
0.4
0.3
0.04
-15.2
-0.2
2.6
-12.6
MP2/HF
-17.6
-4.9
-6.7
-4.3
-1.8
0.4
0.3
0.04
-16.8
-0.4
2.6
-14.2
DFT
-17.9
-5.8
-6.8
-3.8
-1.5
1.0
0.6
0.2
-16.1
-
3.3
-12.8
HF
-9.1
-
-
-
-
0.3
0.3
-
-8.4
0.0
0.9
-7.6
MP2/HF
-10.2
-
-
-
-
0.3
0.3
-
-9.5
0.0
0.9
-8.7
DFT
-11.4
-
-
-
-
0.6
0.7
-
-10.1
-
0.9
-9.3
HF
-14.1
-0.1
-6.8
-7.2
-0.1
0.1
0.3
0.1
-13.6
-0.7
3.5
-10.1
MP2/HF
-17.2
-1.1
-7.5
-8.6
0.0
0.1
0.3
0.1
-16.7
-1.6
3.5
-13.2
DFT
-18.7
-0.1
-9.2
-9.6
0.2
0.5
0.5
0.4
-17.3
-
4.0
-13.3
HF
-10.9
-
-
-
-
0.4
0.3
-
-10.2
0.0
1.3
-8.9
MP2/HF
-13.2
-
-
-
-
0.4
0.3
-
-12.5
0.0
1.3
-11.2
DFT
-14.2
-
-
-
-
1.0
0.6
-
-12.6
-
1.1
-11.5
b
c
c
c
c
e
HF
-20.7
-5.5
-5.2
-7.2
-2.8
0.6
MP2/HF
-22.8
-6.0
-6.2
-7.7
-2.9
DFT
-26.0
-6.8
-6.5
-7.5
HF
-9.9
-
-
MP2/HF
-12.0
-
DFT
-13.2
HF
e
WUC
UC
WUU
UU
WUA
UA
WGA
30
HF
-23.2
-7.0
-8.5
-4.8
-3.0
0.9
0.7
0.2
-21.4
-3.0
3.9
-17.6
MP2/HF
-25.8
-7.8
-9.1
-5.7
-3.2
0.9
0.7
0.2
-24.0
-4.6
3.9
-20.2
DFT
-30.0
-8.7
-9.1
-6.1
-6.0
1.8
1.2
0.9
-26.2
-
3.9
-22.2
HF
-12.8
-
-
-
-
0.5
0.6
-
-11.7
-0.8
1.6
-10.1
MP2/HF
-15.2
-
-
-
-
0.5
0.6
-
-14.1
-1.9
1.6
-12.6
DFT
-16.4
-
-
-
-
1.1
0.8
-
-14.5
-
1.3
-13.1
HF
-21.1
-10.8
-2.3
-6.0
-1.9
0.4
0.9
0.1
-19.6
-0.2
2.6
-17.0
MP2/HF
-21.1
-10.8
-2.6
-5.8
-1.9
0.4
0.9
0.1
-19.6
-0.4
2.6
-17.0
DFT
-22.9
-10.7
-2.4
-6.6
-3.2
0.6
1.4
0.1
-20.8
-
2.1
-18.8
HF
-12.8
-
-
-
-
0.4
0.7
-
-11.8
-0.02
0.8
-10.9
MP2/HF
-13.0
-
-
-
-
0.4
0.7
-
-12.0
-0.2
0.8
-11.1
DFT
-13.8
-
-
-
-
0.5
1.0
-
-12.3
-
1.1
-11.2
HF
-16.7
-
-
-
-
0.4
0.7
-
-15.5
-0.3
0.9
-14.7
MP2/HF
-17.8
-
-
-
-
0.4
0.7
-
-16.6
-0.9
0.9
-15.7
DFT
-18.1
-
-
-
-
0.6
1.0
-
-16.4
-
1.1
-15.4
GA
W371UG
UG
GG
a
The total energies of all water-mediated and direct base pairs are given in the supplementary material.
energy. c ∆EXY, ∆EXW, ∆EYW: Pairwise interaction energies between two components, e. g.
for the interaction energy between U and C. d ∆E3: (Cooperative) three-body term.
e
∆EXY
b
∆E: Interaction
stands in the WUC case
∆EDEF: Deformation energy. In WUU
and WGG X corresponds to U1 and G1 and Y corresponds to U2 and G2, respectively (Fig. 1). f ∆ET=∆E+Σ∆EDEF. g E-Epla:
Energy difference between the optimized nonplanar and planar base pairs.
h
∆E ZPE:
Change in zero point energy upon
complex formation. i ∆E0=∆ET+∆E ZPE.
31
TABLE 8. Cooperative Contributions to Interaction Energies (%) of Water-Mediated
Base Pairs
∆E3/∆Ε (%)
MP2/HF
DFT
WUC
12.6
20.3
WUU
10.0
8.2
WUA
0.3
-1.3
WGA
12.3
20.1
W371UG
9.1
14.1
32
TABLE 9. Differences in Interaction Energies ∆E0 (kcal/mol) Between Water-Mediated
and Direct Base Pairs
MP2/HF
DFT
∆E0(WUC) - ∆E0(UC)
-8.6
-9.8
∆E0(WUU) - ∆E0(UU)
-5.5
-3.5
∆E0(WUA) - ∆E0(UA)
-2.0
-1.8
∆E0(WGA) - ∆E0(GA)
-7.6
-9.1
∆E0(W371UG) - ∆E0(UG)
-5.9
-7.6
33
TABLE 10. Interaction Energies ∆E0 (kcal/mol) for Water-Mediated and Direct Base
Pairs Divided by the Number of H-Bonds (MP2/HF level) a
Water-Mediated
Direct
Base Pair
Base Pair
WUC/UC
-6.06
-4.80
-1.26
WUU/UU
-4.73
-4.35
-0.38
WUA/UA
-4.40 (3 H-bonds)
-5.60
+1.20
-2.64 (5 H-bonds)
-5.60
+2.96
WGA/GA
-6.73
-6.30
-0.43
W371UG/UG
-5.66
-5.55
-0.11
a
Difference
The assumed number of H-bonds is three in the water-mediated pairs and two in the direct pairs. This means that the
bifurcated H-bonds in WGA and W371UG are counted as one H-bond. For WUA data are given with three and five H-bonds.
The different number of H-bonds does not affect the results in a qualitative sense.
34
Supplementary TABLE 1.
The Table lists the absolute values for the energies of the optimized water-mediated and direct
base pairs.
Energy/Hartrees a)
Base Pair
WUC
WUU
WUA
WGA
W371UG
UC
UU
UA
GA
UG
GG
a
HF
MP2/HF
B3LYP
-881.1725023
-901.0162163
-953.0697946
-1080.0123956
-1027.9539857
-805.1301043
-824.9800450
-877.0377213
-1003.9707509
-951.9162425
-1078.8533707
-883.7308074
-903.5784079
-955.9056342
-1083.2897583
-1030.9561673
-807.4905973
-827.3442294
-879.6747815
-1007.0504841
-954.7211045
-1082.1020668
-886.2345234
-906.1099621
-958.6176385
-1086.3697214
-1033.8547212
-809.7911275
-829.6734479
-882.1838984
-1009.9258364
-957.4164722
-1085.1628881
All calculations have been performed with the 6-31G(d,p) basis set.
35
H
H
a)
H
H42
O4
H
C1’
N
N3
H
N4
N3
N
H3
C1’
O2
O2
O
H
H
U
C
WUC
H
b)
H
O
H
H3
O4
H
C1’
N
N3
N3
N
C1’
O2
H3
O
O
H
H
U1
U2
H61
c)
H62
N
H
O2
N3
H
H
N
N6
C1’
WUU
N
N7
H3
N
C1 ’
H8
H
O
O4
H
U
A
WUA
H
d)
H
N
C1’
N
N
N1
N2
N C’
1
H61
O6
H
N
H
N6
N1
H1
O
H22
N
H2
H
H
G
A
WGA
e)
H5
H
O6
H1
O4
C1’ N
N3
O
H22
H3
H
O
N
N1
N2
H
N
N
C1’
H
H
U
G
WUG
f)
H
H
H N
H
N
N
C1’ N
H8
G1
N
N2
H22
O6
H1
C1’
N
H
N1
N
O6
N7
H
O
H
G2
WGG
WUC/UC
WUU/UU
a)
c)
b)
d)
WUA/UA
WGA/GA
e)
g)
f)
h)
WGG/GG
W371UG/UG
i)
WGG: no minimum
j)
k)
a)
W 371
U 74
G 102
W 329
b)
G 100
G 76
W 330
W 312
C5’H5’
A 99
a)
b)